Algorithmically designed lace tessellations

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Creating tapes

Step 1) Draw the path that the tape follows

There are many ways you can draw a path in Inkscape. In the example shown here, I have used the spiral tool, the freehand pencil, and the Bezier pen. At the end of this post, I will discuss additional options.

In this example, I started with the spiral tool. Select the spiral tool () from tool icons along the left side of Inkscape. You can adjust the appearance of the spiral with the options along the top of the Inkscape window (see red box below). For information about each of the values that you can change, take a look at Tav Mjong’s Shapes and Spirals Chapter or the FLOSS manual. In the main drawing area, click and hold down the left button on your mouse and drag the mouse to create the spiral on the canvas. When you have the right size, release the mouse button.

I drew the rest of the heart, using the freehand pencil tool. Select the pencil icon () from the left side of the Inkscape window. You can adjust how the pencil draws using the options along the top of the window. I used the “Regular Bezier Path” mode and increased the “smoothness” to 58 so that, even though my hand shakes a bit when dragging the mouse, the line is smooth. To find out more about the different modes and settings, have a look in Tav Mjong’s Creating Paths Chapter. Click and hold down the left mouse button and drag the mouse to draw your curve. When you are done, release the mouse button. Don’t worry if it is not perfect; you can change the line after you let go of the mouse. I will show you how later on in this tutorial.

Note: If you are going to do a lot of freehand drawing, you might want to consider getting a graphics tablet.

We now have a spiral and a curve but, for drawing the zigzag pattern, we need them to be connected together. Select both the spiral and the freehand curve. To do this, click on the Select and Transform tool (). To select more than one object, you can hold down the Shift key and click on each object, alternatively, you can click and drag the mouse to create a box around both objects (Note: no part of the object can be outside the box). You should see a dashed box around both objects.

From the top menu, select Path -> Combine. Now you should just see one box around both items.

Step 2) Edit Path

Now we can modify the path to get rid of any wobbles.

Select the Edit Path by Nodes tool (). When you select a path, it will display little gray squares or diamonds along the path – these are called nodes. The nodes control the appearance of the path. You can change the position of a node by clicking on it and dragging. You can also change how much the path curves by clicking on a node and pulling on the two little whiskers that appear by the node . You can also add or remove nodes as well as many other options, too many for me to explain in this tutorial. I recommend having a quick look at Tav Mjong’s Path Editing Chapter or in the FLOSS manual.

Step 3) Add zigzags along path

Now that you have the path that you want the tape to follow, it is time to add nicely spaced zigzag lines showing where to put the pins.

The first step is to create one copy of the “zig” (or is it a “zag”?). I used the Bezier pen tool to do this. Start by selecting the pen tool (). To create lines with this tool, click and release the left mouse button at each point in the path you are drawing. A straight line will join the nodes together. To finish the path, double click. You can find out more about the Bezier pen tool from Tav Majong’s: Creating Paths Chapter or the FLOSS manual.

To create the zig, draw an upside down V shape (see below).

To make sure the Λ is perfect, we can edit the nodes using the alignment tool:
First, select the path editing tool (). Next, select Object -> Align and Distribute from the top menu bar of Inkscape. This will open a little toolbox on the right side of the Inkscape window. Click on the Λ to select it. Drag your mouse to select the two little grey boxes at the bottom of the Λ. The boxes should turn blue. Click on the “align to horizontal line” icon (see below) to make the two points line up.

Now drag your mouse to select all of the boxes in the Λ and click on the “distribute horizontally” icon (see below). Now the space between the points should be the same. To find out more about the alignment tool, see Tav’s Align Chapter.

OK, now we have a very nice “zig” so let’s use it. Select the Λ and copy it to the clipboard (Edit -> Copy). Select the path you drew for the tape. From the top menu bar, click on Open -> Path Effects… This will open a toolbox, called “Path Effects”, on the right side of the Inkscape window.

Click on the Plus sign () in the “Path Effects” tool box. A list will pop up. Scroll down the list and click on “Pattern Along Path” and click on the Add button below the list.

Click on the “Link to path on clipboard” button (). Change the “Pattern copies” to “Repeated”. Now you should see zigzags along the path.

You can adjust the size of the zigzags by changing the original Λ. Choose the Selection tool (), click on the Λ and drag the corners of the dashed rectangle () to make the Λ bigger or smaller. If you hold down the Ctrl key while dragging the box, the width and height will scale proportionally. You can also move the zigzags along the path (maybe you don’t like the way the zigzag looks at the bottom point of the heart) by changing the value of “Tangent offset”. To learn about more tricks, take a look at Tav’s Pattern Along Path Chapter or the Floss manual .

4) Fine tune the zigzags

OK, you have played around with the Pattern along path and it is pretty good but you still want to change it a little bit. As a last step, you can turn the pattern along path into an editable path object. Using the selection tool, select the zigzag path and from the top menu choose Path -> Object to Path. This will turn all of the little zigzags into a path with individual nodes.

You can now edit individual nodes the same way we did in Step 2 above.

I didn’t like the way the zigzags became rounded so I went into the Edit Path by Nodes tool (), selected all of the nodes (Ctrl A or drag a rectangle around everything) and clicked on the “Make selected nodes a corner” () option (see A below). This made all of the lines straight. I also dragged some of the nodes so that the different parts of the spiral would be connected together (see B below).

5) Create outline of zigzag

Finally, I wanted a curve along the inside and outside of the tape. I drew this using the Bezier pen tool () similar to what we did in Step 3. I wanted the curve to lie exactly on the nodes of the zigzag so I used Inkscape’s snap to target feature which appears along the right side of Inkscape. This feature has many options so I recommend reading up about it in Tav’s Snapping Chapter. I used “Snap to cusp nodes”.

Once I had finished drawing with the pen tool, the curve was made of straight lines so it did not look nice and smooth. To fix this, I used the Edit Path by Nodes tool (), selected all of the nodes (Ctrl A or drag a rectangle around everything) and clicked on the “Make selected nodes smooth” () option

Now it’s your turn!

Additional notes:

There are many other ways to draw a path. You can draw a shape and convert it to a path. This is very useful if you want to combine circles (or parts of circles) with triangles, squares etc. I recommend reading Tav’s Paths from Objects Chapter.

Instead of zigzags, you could also place dots along a path using the “Pattern along path” technique discussed in Step 3. Just replace the Λ with a circle. Notes: You will need to convert the circle to a path. You will need to set the “Spacing” parameter in the Path Effect Editor to create a gap between the dots.